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Question

Vertex of the parabola whose parametric equation is x=t2t+1,y=t2+t+1;tR, is

A
(1,1)
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B
(2,2)
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C
(12,12)
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D
(3,3)
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Solution

The correct option is A (1,1)
x=t2t+1, y=t2+t+1
x+y=2(t2+1) and yx=2t
x+y2=1+(yx2)2
(yx)2=2(x+y)4
(yx)2=2(x+y2)
Vertex will be the point where the lines
yx=0 and x+y2=0 meets,
x+x2=0x=1y=1
Hence the vertex is (1,1)

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